The async work is picked up again inside the player loop, which also runs outside playmode. As a result the mesh UVs are accessed inside the player loop which rightfully throws an error that read/write should be enabled on the mesh.
The issue can also be reproduced inside the editor although at a much lower rate. In batch mode the application does not spend time redrawing the inspector etc., so the chance of the work getting resumed inside the player loop tick is much higher.